MATHEMATICS COLLEGE

Suppose an interval estimate for the population mean was 62.84 to 69.46. The population standard deviation was assumed to be 6.50, and a sample of 100 observations was used. The mean of the sample was: A. 56.34 B. 62.96 C. 6.62 D. 66.15

Answers

Answer 1

Answer:

Answer: Option D.

Step-by-step explanation:

The given interval for population mean was 62.84 to 69.46.

The sample mean will be at the midpoint of the interval.

That is: $(\left(62.84+69.46\right))/(2)=66.15$ .

Learn more: brainly.com/question/12049968

Answer 2

Answer:

Answer:

$\bar X = 69.46-3.31= 66.15$

$\bar X = 62.84+3.31= 66.15$

Because the confidence interval is defined as $(\bar X -ME, \bar X + ME)$

The best option is : D. 66.15

Step-by-step explanation:

Previous concepts

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

$\bar X$ represent the sample mean (variable of interest)

$\mu$ population mean

$\sigma=6.50$ represent the population standard deviation

n=100 represent the sample size

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma=6.5)$

The sample mean $\bar X$ is distributed on this way:

$\bar X \sim N(\mu, (\sigma)/(√(n)))$

The confidence interval on this case is given by:

$\bar X \pm z_(\alpha/2)(\sigma)/(√(n))$ (1)

We have a confidence interval given (62.84, 69.46). W ecan find the margin of error for this interval with this:

$ME= (69.46-62.84)/(2)=3.31$

With the margin of error we can find the sample mean with this:

$\bar X = 69.46-3.31= 66.15$

$\bar X = 62.84+3.31= 66.15$

Because the confidence interval is defined as $(\bar X -ME, \bar X + ME)$

The best option is : D. 66.15

Related Questions

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Solve for n+4 + n/6=16
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Mary runs 7 miles in 60 minutes. At the same rate, how many miles would she run in 24 minutes?

The data set shows the number of practice free throws players in a basketball competition made and the number of free throws they made in a timed competition.Practice throws 312 614 2 710 8Free throws 10 22 9 35 4 11 28 20A. Use technology to find the equation AND coefficient of determination for each type of regression model. Use the number of practice throws for the input variable and the number of free throws for the output variable. Round all decimal values to three places. Equation of regression modelCoefficient of determinationLinear model Quadratic model Exponential model B. EXPLAIN, using the information you found above, which model best fits the data set. How did you come to your conclusion?Note: write exponents like this x^2 if you need to.

Answers

Let

x -----> number of practice throws

y -----> the number of free throws

Part A

Linear Model

Using a Linear Regression Calculator

we have

ŷ = 2.352X - 0.852

see the attached figure

Remember that

With linear regression, the coefficient of determination is equal to the square of the correlation between the x and y variables

the coefficient r=0.919

Quadratic model

Using a Quadratic regression Calculator

we have

y=0.073x^2+1.205x+2.555

correlation coefficient r=0.925 ------> strong correlation

see the attached figure

Exponential model

Using an Exponential Regression Calculator

we have

y=4.229(1.17)^x

Correlation:r=0.913

see the attached figure

Part B

The model that best fits the data is the Quadratic model because its value of r is greater than the linear model and greater than the exponential model

The dot plot below shows the hourly rate of some babysitters in a city:A number line is shown from 1 dollar to 7 dollars in increments of 1 dollar for each tick mark. The horizontal axis label is Dollars per hour. There are 3 dots above 4 dollars, 2 dots above 5 dollars, 4 dots above 6 dollars, and 1 dot above 7 dollars. The title of the line plot is Babysitting Rates.

Which statement best describes the shape of the data?

It is symmetric and has a peak at $7.00.
It is not symmetric and has a peak at $6.00.
It is a cluster from $1.00 to $7.00 and has gaps.
It is a cluster from $1.00 to $7.00 and has no gaps.

Answers

Answer:

It is not symmetric and has a peak at $6.00

Step-by-step explanation:

Drawn in text in a vertical fashion, we might show it as ...

4 | ooo

5 | oo

6 | oooo

7 | o

The data is clearly not symmetric, has a range from 4 to 7, and has a peak at 6. The appropriate description is ...

It is not symmetric and has a peak at $6.00

Find the product. write your answer in exponential form 9²•9-⁶

Answers

Answer:

9^8

Step-by-step explanation:

9²•9⁶ = 9^(2+6) = 9^8

Answer:

IF the 6 is negative : $9^(2)$ · $9^(-6)$ then the answer is 1/ $9^(4)$

If the 6 is positive then the answer is $9^(8)$

Step-by-step explanation:

Exponents are add when their bases are similar.

Tyrone swam eight less than three times as many laps as Marcia if Tyrone swam 13 laps how many laps did Marcia swim

Answers

Answer:

63 laps

Step-by-step explanation:

Tyrone-13

Marcia-(Tyrone+8)x3

fill in the equation

(13+8)x3

21x3

Answer:

Step-by-step explanation:13+8=21

21x3=63

I hope this helps

Deanna and Lise are playing game at the arcade. Deanna started with $20 and the the game she is playing costs $0.25 each game. Lise started with $40, and her machine costs $0.75 per game. How many games will it be before they both have the same amount of money left? Make an expression the solves the problem.

Answers

Deanna 78 games 19.50

Lisa 26 games 19.50

Hope that helps..

Final answer:

To determine how many games it will take for Deanna and Lise to have the same amount of money left, set up an equation using their net losses per game and solve for 'g'. It will take 40 games for them to have the same amount of money left.

Explanation:

To determine how many games it will take for Deanna and Lise to have the same amount of money left, we need to set up an equation. Let's start by determining their net loss per game by subtracting the cost of each game from their initial amount of money. For Deanna, her net loss per game is $0.25. For Lise, her net loss per game is $0.75.

Let's represent the number of games they play with the variable 'g'. To find the number of games it will take for them to have the same amount of money left, we need to set up an equation. Deanna's remaining money after 'g' games can be represented as $20 - $0.25g. Lise's remaining money after 'g' games can be represented as $40 - $0.75g.

Setting the two expressions equal to each other, we can solve for 'g':

$20 - $0.25g = $40 - $0.75g

$20 = $40 - $0.5g

$0.5g = $20

g = $20 / $0.5 = 40

Therefore, it will take 40 games before Deanna and Lise have the same amount of money left.

The scores on a test are normally distributed. The mean of the test is 750 and the standard deviation is 70. By using the Empirical rule, what scores fall 3 standard deviations from the mean?

a.610 and 820

b.610 and 960

c.680 and 820

d.540 and 960

Answers

I think it will be B 610 and 820 but im not sure.
Hope This Helps!
~Cupcake

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